In this section, I load data for the baseline calibration using the linear and linear quadratic cost models.
| params | value | concept | units |
|---|---|---|---|
| alpha | 1625836.98 | Demand model : intercept | USD |
| beta | 1563.75 | Demand model : coefficient | USD/metric ton of biomass |
| r | 0.20 | Intrinsic growth rate | unitless |
| k | 20226.00 | Carrying capacity (in metric tons) | metric tons of biomass |
| sigma | 0.00 | Catchability | % of biomass/vessel trip |
| avg_cost | 14386.69 | Average cost per vessel trip at historical value | USD/vessel trip |
| W_high | 3.75 | Quadratic cost parameter - Quadratic cost function | USD vessel trip\(^{-2}\) |
| fixed_cost | 13811222.14 | Fixed cost - Quadratic cost function | USD |
| W1 | 13012.59 | Linear cost parameter - Linear quadratic cost function | USD/vessel trip |
| W2 | 0.75 | Quadratic cost parameter - Linear quadratic cost function | USD vessel trip\(^{-2}\) |
| age | 4.50 | Age of farmed totoaba | Years |
| gamma | 1354.25 | Demand model : substitutable good coefficient | USD/metric ton of biomass |
| v | 89929.92 | Unit cost of farming | USD/metric ton of biomass |
| i_r | 0.10 | Interest rate | % |
| c | 0.00 | Unit cost of trading | USD/ metric ton of biomass |
Define function where variable is either x i.e
population stock, or s i.e price paid to poachers. All the
parameters take default values specified in the global environment.
growth(x, ...) : logistic growth function, yields
growth of population (in metric tons)
pt_harvest(x,...) : harvest (in metric tons) when
trader is price taker
monop_harvest(x, ...): harvest (in metric tons) when
trader is a monopolist
monop_harvest_lq(x, ...): harvest (in metric tons)
when trader is a monopolist and cost structure is linear
quadratic
cournot_harvest(x, ...),
bertrand_harvest(x, ...): harvest (in metric tons) when
trader and farmer compete in Cournot, i.e, set quantities
strategically, and Bertrand, i.e, set prices
strategically.
cournot_harvest_lq(x, ...),
bertrand_harvest_lq(x, ...) : harvest (in metric tons) when
trader and farmer compete in Cournot i.e, set quantities
strategically, and Bertrand i.e, set prices strategically and
cost structure is linear quadratic
price_poachers_cournot(x, ...),
price_poachers_bertrand(x, ...): price paid to poachers (in
USD/metric tons) when trader and farmer compete in Cournot and
Bertrand
cournot_farmed(s, ...),
bertrand_farmed(s, ...): quantity farmed (in metric tons)
when trader and farmer compete in Cournot and
Bertrand
Generate results saved at
~/data/outputs/results_all_models.csv :
W_lq_new: each row corresponds
to a cost parameter \(W\), \(W_1\) and \(W_2\)To understand the impact of different \(W_1\) & \(W_2\) divides :
Clearly, the choice of \(W_1\) and \(W_2\) is important with respect to the anticipated equilibrium in the vertical monopoly case : with a linear-quadratic cost function, we no longer can say the monopoly will achieve a healthy steady state population. The results in the post intervention world are robust to the cost specification, and guarantee population increases in the quantity adjustment scenario, while population may marginally diminish in the price setting scenario.
First, illustrate the new equilibria with the same \(W\) = 3.7465338 value and the prefered solution for \(W_1\) and \(W_2\) (e.g 13012.59, 0.75) in the linear quadratic cost of effort specification.
Define bio-economic performance by combining population variables (stock and harvest) with price and profit data from economic model.
| Scenario | Poached harvest (in mt) | Farmed harvest (in mt) | Steady state population (in mt) | Retail price (in USD/ton of buche) | Retail price of 500g buche (in USD) | Price paid to poacher (in USD/ton of buche) | Poacher price of 500g buche (in USD) | Illegal profit (in million USD) | Farming profit (in million USD) | Fishing profit (in million USD) | Aggregate profit (in million USD) | Aggregate profit change (in million USD) | Farming profit change (in million USD) | Illegal profit change (in million USD) | Fishing profit change (in million USD) | Variation in ss. pop. | Poaching change (%) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Vertical Monopoly | 509.64 | 0.00 | 17259.0 | 828894.3 | 21302.583 | 31951.60 | 821.1560 | 406.15 | 0.00 | 8.14 | 414.29 | 12.61 | 0.00 | 6.07 | 6.54 | -0.16% | 0.76% |
| Quantity adjustment | 369.87 | 330.94 | 18182.0 | 599279.2 | 15401.476 | 20894.42 | 536.9866 | 213.93 | 171.26 | 3.86 | 389.05 | -12.63 | 171.26 | -186.15 | 2.26 | 5.18% | -26.88% |
| Price setting | 520.27 | 425.30 | 17184.0 | 236298.3 | 6072.866 | 32903.89 | 845.6299 | 105.82 | 70.71 | 8.56 | 185.09 | -216.59 | 70.71 | -294.26 | 6.96 | -0.59% | 2.86% |
| Vertical Monopoly - LQ cost | 505.81 | 0.00 | 17286.0 | 834873.3 | 21456.245 | 43909.71 | 1128.4797 | 400.08 | 0.00 | 1.60 | 401.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0% | 0% |
| Quantity adjustment - LQ cost | 362.46 | 334.15 | 18228.0 | 606518.8 | 15587.534 | 39717.45 | 1020.7385 | 205.44 | 174.60 | 0.74 | 380.78 | -20.90 | 174.60 | -194.63 | -0.86 | 5.45% | -28.34% |
| Price setting - LQ cost | 536.94 | 432.53 | 17257.5 | 200446.5 | 5151.475 | 43506.01 | 1118.1043 | 84.27 | 57.26 | 4.41 | 145.94 | -255.74 | 57.26 | -315.81 | 2.81 | -0.16% | 6.15% |
Table for manuscript :
| Scenario | Poached harvest (in mt) | Farmed harvest (in mt) | Steady state population (in mt) | Illegal profit (in million USD) | Farming profit (in million USD) | Fishing profit (in million USD) | Aggregate profit (in million USD) | Illegal profit change (in million USD) | Variation in ss. pop. | Poaching change (%) |
|---|---|---|---|---|---|---|---|---|---|---|
| Vertical Monopoly | 505.81 | 0.00 | 17286.0 | 400.08 | 0.00 | 1.60 | 401.68 | 0.00 | 0% | 0% |
| Quantity adjustment | 362.46 | 334.15 | 18228.0 | 205.44 | 174.60 | 0.74 | 380.78 | -194.63 | 5.45% | -28.34% |
| Price setting | 536.94 | 432.53 | 17257.5 | 84.27 | 57.26 | 4.41 | 145.94 | -315.81 | -0.16% | 6.15% |